I have observed that if one takes a whole number, between 10 and 9999, then re-arranges the digits in any way. Then, one subtracts the lesser number from the greater, the answer is always divisible by three. Eg let 5124 be original number. Re-arranged to be 4512. 5124 - 4512 = 612, which is divisible by three.
Is there a proof as to why this is so?
Many thanks if anyone can help
Not only is the number divisible by 3 its divisible by 9!
Say be a number. And let be a permutation of its digits.
Thankyou for the proof which i confess, is too complicated for me to follow. Is there any prospects of breaking down the steps further. If not, thankyou anyway and i will try and decipher.
Are you familar with the basic laws of modular arithmetic?
Originally Posted by c0unsel
Unfortunately not. However, in the event that the same proves too complex to explain a suitable link would be gratefully digested.
Maybe this is a little too advanced.